Reduce to lowest terms: $- \dfrac{1}{5} \div \dfrac{7}{4} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{7}{4}$ is $ \dfrac{4}{7}$ Therefore: $ - \dfrac{1}{5} \div \dfrac{7}{4} = - \dfrac{1}{5} \times \dfrac{4}{7} $ $ \phantom{- \dfrac{1}{5} \times \dfrac{4}{7}} = \dfrac{-1 \times 4}{5 \times 7} $ $ \phantom{- \dfrac{1}{5} \times \dfrac{4}{7}} = \dfrac{-4}{35} $